This invention relates to machines for wrapping elongated articles with tape and/or warp material and is particularly suited to wrapping articles such as real or artificial flower stems. In the floral industry, it is often desirable to wrap the stems of flowers with tape and assemble a number or individual components such as blossoms, buds, leaves, etc. around a wire core. In the case of real flowers, such wrapping may serve to strengthen the relatively fragile stem portion of the flower which may then be incorporated into suitable floral arrangements such as corsages or bouquets. Similarly, in the case of artificial flowers, leaves or a number of flowers may be joined together by wrapping their stems with tape. A warp or thread material may also be used for providing strength to the wrapping and other decorative effects. Floral arrangements such as wreaths, canole rings, garlands or leis may be formed by continuously joining a chain of flowers together by wrapping their stems to a continuous wire core with the flowers or leaves being axially displaced relative to one another. In the past, such winding of floral arrangements has been primarily accomplished by hand since a suitable apparatus for wrapping has not been available.